Subdifferentials, faces, and dual matrices

DOI10.1016/0024-3795(93)90209-7zbMath0772.15014OpenAlexW2114236395MaRDI QIDQ2365719

Krystyna Ziętak

Publication date: 29 June 1993

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(93)90209-7

zbMATH Keywords

unitarily invariant normsdual matricesfaces of the unit ball of matricessubdifferentials of matrix norms

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60)

Related Items (13)

Low-rank matrix recovery with Ky Fan 2-\(k\)-norm ⋮ Properties of linear approximations of matrices in the spectral norm ⋮ Unnamed Item ⋮ Subdifferential set of the joint numerical radius of a tuple of matrices ⋮ A Corrected Tensor Nuclear Norm Minimization Method for Noisy Low-Rank Tensor Completion ⋮ Uniqueness in nuclear norm minimization: flatness of the nuclear norm sphere and simultaneous polarization ⋮ Birkhoff-James orthogonality and applications: a survey ⋮ Sensitivity and Backward Perturbation Analysis of Multiparameter Eigenvalue Problems ⋮ On the extremal structure of least upper bound norms and their dual ⋮ Sensitivity Analysis of Nonlinear Eigenproblems ⋮ On approximation problems with zero-trace matrices ⋮ Convex analysis on Cartan subspaces. ⋮ On matrix approximation problems with Ky Fan \(k\) norms

Cites Work

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• Constructing all smallest simultaneous confidence sets in a given class, with applications to MANOVA
• Faces in the unit ball of the dual of \({\mathcal L}({\mathbb{R}}^ n)\)
• On the characterization of the extremal points of the unit sphere of matrices
• On the geometry of the unit ball of unitary matrix spaces
• Characterization of best approximations in normed linear spaces of matrices by elements of finite-dimensional linear subspaces
• Characterization of the subdifferential of some matrix norms
• Facial structures of schattenp-Norms
• Maximum Properties and Inequalities for the Eigenvalues of Completely Continuous Operators

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